Question

Which term of an AP 3, 9, 15, 21 ....... is 147.​

Answer 1

-3,3,9,15,21

Your input -3,3,9,15,21 appears to be an arithmetic sequence

Find the difference between the members

a2-a1=3--3=6

a3-a2=9-3=6

a4-a3=15-9=6

a5-a4=21-15=6

The difference between every two adjacent members of the series is constant and equal to 6

General Form: a

n

=a

1

+(n-1)d

a

n

=-3+(n-1)6

a1=-3 (this is the 1st member)

an=21 (this is the last/nth member)

d=6 (this is the difference between consecutive members)

n=5 (this is the number of members)

Sum of finite series members

The sum of the members of a finite arithmetic progression is called an arithmetic series.

Using our example, consider the sum:

-3+3+9+15+21

This sum can be found quickly by taking the number n of terms being added (here 5), multiplying by the sum of the first and last number in the progression (here -3 + 21 = 18), and dividing by 2:

n(a1+an)

2

5(-3+21)

2

The sum of the 5 members of this series is 45

This series corresponds to the following straight line y=6x+-3

@ Anirudh Mall